Symmetric residue pyramids - an extension of Burt Laplacian pyramids

The Laplacian pyramid was proposed as a compact image code by Burt (1983). However, it is shown that it does not achieve optimal signal compaction due to significant overlap between subbands in the frequency domain. In addition, it also leads to a slightly redundant signal representation. An extension of the Laplacian pyramid is proposed that exploits this redundancy to achieve better signal compaction. In contrast to the unidirectional fine to coarse approach used by all multiscale representations, the proposed signal representation adopts a bi-directional approach. Each subband finally depends on both its coarser and finer neighboring subbands. The representation is symmetric in the sense that each subband is a product of an approximation process (based on a finer approximation) as well as a prediction process (based on a coarser approximation). Applications are in the areas of image characterisation, zooming and compression.